10x-1=2/1x-3

Solution for 10x-1=2/1x-3 equation:

10x-1=2/1x-3

We move all terms to the left:

10x-1-(2/1x-3)=0


Domain of the equation: 1x-3)!=0

x∈R


We get rid of parentheses

10x-2/1x+3-1=0

We multiply all the terms by the denominator


10x*1x+3*1x-1*1x-2=0

Wy multiply elements

10x^2+3x-1x-2=0

We add all the numbers together, and all the variables

10x^2+2x-2=0

a = 10; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·10·(-2)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*10}=\frac{-2-2\sqrt{21}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*10}=\frac{-2+2\sqrt{21}}{20}
$